I think fear is an important part of the path, whether it be fear of getting "sucked in", fear of feeling hopeless, or fear of genuinely feeling another's suffering if you stop to have a conversation. As Pema Chödrön said, "Fear is a natural reaction to moving closer to the truth." I'm guilty of all of the things people have said so far, not making eye contact, crossing the street, ignoring... Don't discount the merit of realizing you're doing these things and also realizing it's a form of protecting your heart. There is merit to be had and dedicated in the mere act of seeing your own tendency to protect yourself from suffering. It's something we have in common with uncountable beings. Use this fear as another reminder of interdependence, and especially as a steppingstone to really get at those sides of ourselves we're so good at hiding
Poison into the path of bodhi.
With enough of this kind of thought, you may one day feel you're up to the task of making eye contact, smiling, saying hi and asking their name. Even this is of immesurable benefit, especially for those who are used to being marginalized and shunned. If you feel their pain deeply, it's no less than Chenrezig or your own compassion pointing out that this is another being, more like you than not, and ultimately someone who was once your mother or your child. Anyone would be distraught seeing someone they love suffering from mental illness or deplorable living conditions. And relatively, all of these people ARE beings who were once or still are loved dearly by someone else. How unfortunate that any being still suffers, especially so deeply and visibly! It really breaks your heart
Since most of us aren't social workers or millionaires with ample resources, we have to help in other ways. And as fellow samsaric beings, what we offer can seem like a drop in a huge ocean of suffering. Who cares about the aspiration to relieve this person's suffering if all we do is smile at them and go on our way? It matters because even this small aspiration is rare among samsaric beings. This thought, "This being, my mother, is suffering. May they be free." goes much farther than others who feel a fleeting pity or most who ignore them completely. Even a pitiful drop of merit, like karma generally, will grow and grow if in a conducive environment, and luckily the Three Jewels are such an environment. Accumulate every little scrap of merit, every little compassionate thought, and dedicate it to these others in such bad need of it.
If we already had perfect wisdom and perfect compassion, we wouldn't be here in the first place. So like the poor woman who could offer only a single butter lamp, but whose lamp kept shining long after all the others, let's not discount the value of working on our compassion and our wisdom in whatever capacity we can. Merit, dedicate, merit, dedicate, practice your ass off for these suffering beings. Eventually your bucket of tiny slivers of jewels will be full. Then we'll all be guru Buddhas and know just what to do! That'll be the day
Until then, don't worry and do your best
What else are you gonna do??